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Endogenous discounting and the domain of the felicity function

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  • Schumacher, Ingmar

Abstract

The objective is to show that endogenous discounting models should use a felicity function constrained to a positive domain. A variety of articles use the Mangasarian or Arrow and Kurz condition as a sufficient condition for optimality, which restricts felicity to a negative domain. Since the level of the felicity function shows up in the optimal path it leads to qualitatively different solutions when one uses a negative or positive felicity function. We suggest reasons why the domain should be positive. We furthermore derive sufficiency conditions for concavity of a transformed Hamiltonian if the felicity function is assumed to be positive.

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Bibliographic Info

Article provided by Elsevier in its journal Economic Modelling.

Volume (Year): 28 (2011)
Issue (Month): 1-2 (January)
Pages: 574-581

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Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:574-581

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Web page: http://www.elsevier.com/locate/inca/30411

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Keywords: Endogenous time preference Optimality Recursive utility Felicity;

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References

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  1. Ingmar, SCHUMACHER, 2006. "Endogenous Discounting via Wealth, Twin-Peaks and the Role of Technology," Discussion Papers (ECON - Département des Sciences Economiques), Université catholique de Louvain, Département des Sciences Economiques 2006059, Université catholique de Louvain, Département des Sciences Economiques.
  2. Palivos, Theodore & Wang, Ping & Zhang, Jianbo, 1997. "On the Existence of Balanced Growth Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 205-24, February.
  3. Becker, Robert A & Boyd, John H, III, 1992. "Recursive Utility and Optimal Capital Accumulation II: Sensitivity and Duality Theory," Economic Theory, Springer, Springer, vol. 2(4), pages 547-63, October.
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  5. Becker, Gary S & Mulligan, Casey B, 1997. "The Endogenous Determination of Time Preference," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 112(3), pages 729-58, August.
  6. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 27(10), pages 1881-1898, August.
  7. David Fielding & Sebastian Torres, 2009. "Health, Wealth, Fertility, Education, and Inequality," Review of Development Economics, Wiley Blackwell, Wiley Blackwell, vol. 13(1), pages 39-55, 02.
  8. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
  9. Becker, Robert A. & Boyd, John III & Sung, Bom Yong, 1989. "Recursive utility and optimal capital accumulation. I. Existence," Journal of Economic Theory, Elsevier, Elsevier, vol. 47(1), pages 76-100, February.
  10. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 91(4), pages 611-35, August.
  11. Maurice Obstfeld, 1989. "Intertemporal Dependence, Impatience, and Dynamics," NBER Working Papers 3028, National Bureau of Economic Research, Inc.
  12. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, Elsevier, vol. 41(1), pages 68-95, February.
  13. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 11(02), pages 272-289, April.
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Cited by:
  1. Ingmar Schumacher, 2009. "Endogenous discounting via wealth, Twin-Peaks and the role of technology," Working Papers hal-00356233, HAL.
  2. Camacho, Carmen & Saglam, Cagri & Turan, Agah, 2013. "Strategic interaction and dynamics under endogenous time preference," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 291-301.
  3. Ingmar Schumacher, 2012. "Political Stability, Corruption and Trust in Politicians," Working Papers hal-00763327, HAL.

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